On ghost fluid method-based sharp interface level set method on a co-located grid and its comparison with balanced force-based diffuse interface method

Abstract

This paper, on Computational multi-Fluid Dynamics (CmFD) development, presents an extension of the Ghost Fluid Method (GFM)-based Sharp Interface Level Set Method (SI-LSM) (originally proposed on a staggered grid) for a co-located grid system. Further, this paper presents a comparative study for the GFM-based SI-LSM and a balanced force method (BFM)-based Diffuse Interface Level Set Method (DI-LSM). The BFM-based DI-LSM avoids a pressure-interfacial force decoupling, during the implementation of the MIM, by a proper-discretization of the surface tension term; not needed for the single-phase flow. Whereas, the GFM-based SI-LSM implicitly couples two immiscible, incompressible fluids via interface jump condition, which makes the Momentum Interpolation Method (MIM) for the two-fluid flow same as that for a single-fluid flow. A unified, for both SI-LSM and DI-LSM, mathematical and numerical formulations are presented. Order of accuracy is demonstrated in-between first-order and second-order; similar to that reported earlier for the various CmFD methods. Finally, validation and relative-performance study are presented for four test cases: static droplet, dam break, drop coalescence, and Rayleigh-Taylor instability. For the static droplet, the relative-performance of the present SI-LSM as compared to the DI-LSM is found similar to that in the literature for SI-VOF (Volume of Fluid) method as compared to DI-VOF method. For the various test cases, superior performance is demonstrated for the SI-LSM as compared to DI-LSM. This paper presents a broader perspective to the MIM for a single-versus-two fluid-flow and diffuse-versus-sharp approaches; and a novel GFM-based SI-LSM on a co-located grid.